Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory

  title={Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory},
  author={Tomoya Naito and Daisuke Ohashi and Haozhao Liang},
  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn--Sham method and the density functional perturbation theory. Difference between the known EDF and the exact one is treated as the first-order perturbation. As benchmark calculations, we reproduce the theoretical exchange and correlation functionals in the local density approximation. Systems of noble-gas atoms are used for benchmark calculations, and the… 

Figures and Tables from this paper

Nuclear energy density functionals from empirical ground-state densities
A model is developed, based on the density functional perturbation theory and the inverse KohnSham method, that can be used to improve relativistic nuclear energy density functionals towards an exact
How to Improve Functionals in Density Functional Theory? —Formalism and Benchmark Calculation—
We proposed in Ref. [arXiv:1812.09285v2] a way to improve energy density functionals in the density functional theory based on the combination of the inverse Kohn-Sham method and the density
Complete solution to the inverse Kohn-Sham problem: From the density to the energy
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground
Building Kohn–Sham Potentials for Ground and Excited States
  • Louis Garrigue
  • Mathematics
    Archive for Rational Mechanics and Analysis
  • 2022
. We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ , there exist potentials having k th excited
Inverse Kohn-Sham Density Functional Theory: Progress and Challenges.
New ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions are introduced.
First step in the nuclear inverse Kohn-Sham problem: From densities to potentials
Nuclear Density Functional Theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant
Kohn-Sham Inversion Toolkit
This work implements the KS inversion methods of Zhao-Morrison-Parr and Wu-Yang in a framework which simplifies analysis and conversion of the resulting potential in real-space.
Insight For The Construction of R-T Phase Boundary in KNN Piezoceramics From The View of Energy Band Structure
The crystal structures and associated energy band structures of classic lead-based PZT (PbZr0.5Ti0.5O3) and lead-free KNN (K0.5Na0.5NbO3) piezoelectric ceramics prepared by a solid-state method are
Toward ab initio charge symmetry breaking in nuclear energy density functionals
Tomoya Naito (内藤智也),1, 2, ∗ Gianluca Colò,3, 4, † Haozhao Liang (梁豪 兆),1, 2, ‡ Xavier Roca-Maza,3, 4, § and Hiroyuki Sagawa (佐川弘幸)5, 2, ¶ Department of Physics, Graduate School of Science, The


Exact Kohn-Sham scheme based on perturbation theory.
  • Görling, Lévy
  • Chemistry
    Physical review. A, Atomic, molecular, and optical physics
  • 1994
An exact formal Kohn-Sham scheme is derived with the help of perturbation theory through the introduction of a basis set and an exact basis set ``exchange-only'' method is obtained.
Numerical methods for the inverse problem of density functional theory
The inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of
A long-range correction scheme for generalized-gradient-approximation exchange functionals
We propose a new long-range correction scheme that combines generalized-gradient-approximation (GGA) exchange functionals in density-functional theory (DFT) with the ab initio Hartree–Fock exchange
Density functional theory is straying from the path toward the exact functional
The energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals, were found to become closer to the exact ones until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
Functional renormalization-group calculation of the equation of state of one-dimensional uniform matter inspired by the Hohenberg-Kohn theorem
We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) of an infinite nuclear matter (NM) in (1+1)-dimensions
Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms
Using accurate correlated wave functions calculated earlier by Bunge and by Larsson, we have constructed the Hohenberg-Kohn-Sham density functionals and exchange-correlation (ground-state) potentials
Exact Kohn-Sham Exchange Potential in Semiconductors
A new Kohn-Sham method that treats exchange interactions within density functional theory exactly is applied to Si, diamond, GaN, and InN. The exact local exchange potential leads to significantly
Density-functional exchange-energy approximation with correct asymptotic behavior.
  • Becke
  • Physics
    Physical review. A, General physics
  • 1988
This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.